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I'm reading the "Mathematical typesetting table" from MS which has been incorporated into the Standard for Open Type Fonts recently.

In the section MATH – Table organization and structure there is a paragraph I couldn't understand:

When designing a MATH table, device tables may be specified for many values used for positioning elements of a formula, suggesting many device corrections. However, a math handling engine may not permit those corrections to accumulate. This accumulation will result in formula dimensions that are significantly different from scaled-down dimensions of the same formula rendered on a high-resolution device. Therefore, accumulation is undesirable and leads to inconsistencies between screen and print versions, as well as possible clipping.

What do they mean by corrections to accumulate above?

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haven't read that document thoroughly, but i interpret this text to mean that it's sometimes necessary to shift a character or element to align with the device raster, and this changes its position relative to other elements in a math expression. if subsequent shifts (corrections) are all made in the same direction, the visual output might look substantially different from what is intended. therefore, care must be taken to "zero out" the effect of the corrections as soon as possible. – barbara beeton Feb 4 at 19:45
The close voters, this seems on topic to me, it's exactly the sort of thing anyone setting up an extended tex for setting math with opentype fonts has to worry about. – David Carlisle Feb 4 at 20:13
up vote 8 down vote accepted

A similar thing came up the other day with Hàn Thế Thành describing how pdftex avoids the accumulation of errors.


Basically if there is a small relative space specified the renderer may have to adjust that to the nearest pixel, but should keep track of how far it is from the ideal position so that at the next relative space it can take the nearest pixel to the ideal position, otherwise if a formula has 50 shifts of .6 of a pixel and they all round to 1, it will be 24 pixels out at the right hand side which is starting to be noticeable.

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That's clear. But there's still one thing I don't understand. The alluded paragraph mentions a "device table", but I couldn't find this table in the [specification] (microsoft.com/typography/otspec/math.htm). Could you clarify this? – Ayrosa Feb 4 at 20:21
i should put you in touch with Murray, it's not really my area, but anyway this file explains they are tables of device-specific settings of various sorts "Example 9 at the end of this chapter uses a Device table to define the minimum extent value for a math script." microsoft.com/typography/otspec/chapter2.htm – David Carlisle Feb 4 at 20:27
Thanks a lot. I really appreciate that. – Ayrosa Feb 4 at 20:28
In reference to the close votes, what would be a proper site to make questions about this math table? – Ayrosa Feb 4 at 20:32
@Ayrosa despite the fact that I just got it re-opened it's sort of marginal here. To be honest you might be best to ask on www-math@w3.org list (which doesn't take so many technical questions but it would be on topic) Or pop over to Murray's blog and put something in the comments he could certainly direct you to the right forum:-) blogs.msdn.com/b/murrays/archive/2014/04/27/… – David Carlisle Feb 4 at 20:39

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